The terminal point determined by t on the unit circle is given by (cos(t), sin(t)).
The terminal point determined by -t:
The point determined by -t is given by (cos(-t), sin(-t)). By the identity sin(-t) = -sin(t), and cos(-t) = cos(t), the terminal point determined by -t is (cos(t), -sin(t)).
The terminal point determined by t + 4π:
The point determined by t + 4π is given by (cos(t + 4π), sin(t + 4π)). By the identity sin(t + 2π) = sin(t) and cos(t + 2π) = cos(t), the terminal point determined by t + 4π is (cos(t), sin(t)).
The terminal point determined by t - π:
The point determined by t - π is given by (cos(t - π), sin(t - π)). By the identity sin(t - π) = -sin(t) and cos(t - π) = -cos(t), the terminal point determined by t - π is (-cos(t), -sin(t)).
The terminal point determined by t + π:
The point determined by t + π is given by (cos(t + π), sin(t + π)). By the identity sin(t + π) = -sin(t) and cos(t + π) = -cos(t), the terminal point determined by t + π is (-cos(t), sin(t)).
The terminal point determined by π - t:
The point determined by π - t is given by (cos(π - t), sin(π - t)). By the identity sin(π - t) = sin(t) and cos(π - t) = -cos(t), the terminal point determined by π - t is (-cos(t), sin(t)).
If the terminal point determined by t is (-3/5, 4/5), then:
The terminal point determined by -t is (3/5, -4/5).
The terminal point determined by t + 4π is (-3/5, 4/5).
The terminal point determined by t - π is (3/5, -4/5).
The terminal point determined by t + π is (3/5, -4/5).
The terminal point determined by π - t is (3/5, -4/5).
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Determine whether y varies directly with x. If so find the constant of variation k and write the equation.
x y
4 6.4
7. 11.2
10 16
13. 20.8
The variable y varies directly with x and the equation is y = 1.6x
How to determine whether y varies directly with xFrom the question, we have the following parameters that can be used in our computation:
x y
4 6.4
7. 11.2
10 16
13. 20.8
From the table above, we can see that;
The y values is 1.6 multiplied by the x values
This implies that the equation is a direct variation
So, we have the equation to be
y = 1.6x
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Let x represent the length of cars in a parking lot. This would be considered what type of variable: Lagging Nonsensical Discrete Continuous
In a parking lot, let x stand in for the length of the vehicles. This would be regarded as a discrete form of variable.
What exactly are discrete variables?
The procedure used to ascertain a discrete variable's value is counting. One illustration is the number of students present. how many red marbles there are in the jar. How many heads are present after the flip of three coins? students' grade level.
The discrete distributions most frequently used by statisticians and analysts are the multinomial, Poisson, Bernoulli, and binomial distributions. There are further instances, including the negative binomial distribution and the geometric and hypergeometric distributions.
The number of vehicles in the parking lot is a discrete numerical variable rather than a continuous one because there are only a finite number of possible values rather than an infinite number and because it must be an integer and cannot be a value between integers. In this instance, discretion is the best course of action.
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Question 5: Matrix Representation of Linear Regression Recall the linear regression problem from previous statistics class: Suppose that we observe 3 observations (Yi, x),(½, x2),(⅓,Xs) and they take values (0.3,1), (0.8,2), (-0.3,0.1). The matrix representation of linear regression is Then Y (0.3,0.8,-0.3)T and β = (A ,A) . what is X in this case? Calculate β-(XTX)-1XTY using R
The problem's matrix representation of linear regression is written as =ε = [ε1 ε2 ε3]'.
Explain about the Linear Regression?A variable's value can be predicted using linear regression analysis depending on the value of some other variable.
The dependent variable is the one you want to be able to forecast.The independent variable is the one you're using to make a prediction about the value of the other variable.Y = Xβ + ε, where Y is indeed the n x 1 vector of a dependent variable, can be used to describe the linear regression issue as a matrix (Yi),
X is the independent variables' n x k matrix (xi),is the coefficients vector of size k by 1, andThe error vector is a n by 1 matrix.With n = 3 (observations), k = 2 (independent variables), and a matrix representation of a issue, the following can be written:
Y = Xβ + ε
Y = [0.3 0.8 -0.3]
X = [1 1 1; 1 2 0.1]
β = [β0 β1]'
ε = [ε1 ε2 ε3]'
Thus, the problem's matrix form is written as =ε = [ε1 ε2 ε3]'.
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perimeter of a triangle
Perimeter of a triangle is the sum of the lengths of it's sides.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Perimeter of a straight sided figure is the total length of it's boundary.
A triangle has three sides.
Length of the boundary of the triangle is the sum of the lengths of it's sides.
If the length of sides of a triangle are a, b and c,
Perimeter = a + b + c
If the triangle is equilateral,
Perimeter = 3a, since all the sides are equal.
Hence the perimeter of the triangle is the sum of the length of the boundary of it.
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Need help on this asap it’s math pre-calculus
The trigonometric ratios and the graph of the periodic function indicates that we get;
1. sin(θ) = -√(13)/7, csc(θ) = -7·√(13)/13
cos(θ) = 6/7, sec(θ) = 1 1/6
tan(θ) = -√(13)/6, cot(θ) = -6·√(13)/13
2. Vertical shift = 4
Amplitude = 3
Period = 6
Equation; y = 3·sin((π/3)·(x - 1.5)) + 4
What is a periodic function?A periodic function is one in which the values of the function are repeated at regular intervals. Trigonometric functions, such as sinusoidal functions are periodic functions.
1. sin(θ) = -√(13)/7
csc(θ) = 1/sin(θ), therefore;
csc(θ) = 1/(-√(13)/7) = -7/√(13) = -7·√(13)/13
csc(θ) = -7·√(13)/13
sin(θ) = Opposite/Hypotenuse
3·π/2 < θ < 2·π, therefore, θ is in quadrant IV
Making use of the proportional or comparative dimensions of the corresponding lengths in a unit circle, we get;
Relative length of the hypotenuse = 7 units
Relative length of the opposite side = -√(13)
The Pythagorean Theorem, indicates that the adjacent side can be found as follows;
Length of the adjacent side = √(7² - 13) = 6
cos(θ) = Adjacent/Hypotenuse
Therefore;
cos(θ) = 6/7sec(θ) = 1/cos(θ), therefore;
sec(θ) = 1/(6/7) = 7/6 = 1 1/6
sec(θ) = 1 1/6tan(θ) = sin(θ)/cos(θ)
Therefore; tan(θ) = (-√(13)/7)/(6/7) = -√(13)/6
tan(θ) = -√(13)/6cot(θ) = 1/tan(θ), therefore;
cot(θ) = 1/(-√(13)/6) = -6/√(13) = -6·√(13)/13
cot(θ) -6·√(13)/13
2. The vertical shift is the vertical displacement of the midline above the x-axis, which can be found as follows;
The location of the midline = (Peak value + Minimum point)/2
Therefore, the location of the midline = (7 + 1)/2 = 4
The vertical shift = 4The period = 1/Frequency
The frequency = Number of cycles per second
The graph indicates that in 1 unit, the cycle completed = 1/6
Therefore; Frequency = 1/6
Period = 1/(1/6) = 6
The period = 6The amplitude is the the distance from the peak to the midline, therefore;
The amplitude = 7 - 4 = 3The equation of the form of a sinusoidal function; y = A·sin(B·(x + C)) + D, indicates that we get;
A = The amplitude = 3
Period = 2·π/B, therefore;
6 = 2·π/B
B = 2·π/6 = π/3
D = The vertical shift = 4
When x = 0, y = 7 = Highest value, therefore;
sin((π/3)·(0 + C)) = sin(π/2)
π·C/3 = π/2
C/3 = 1/2
C = 3 × 1/2 = 3/2 = 1.5
The equation is therefore;
y = 3·sin((π/3)·(x + 1.5)) + 4A vertical reflection of a function, f(x) is -f(x). The leading coefficient of the equation is positive, therefore, there are no vertical reflection or flip
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Rodrigo's hair is 10 2/7 inches long. The barber trims 1/4 inch. About how long is his his hair now ?
Determine the truth value of the following statements if the universe of discourse of each variable is the set of real numbers. Enter your answer as Tor F. 1. 3xVy(xy = 0) 2. 3x (x2 = -1) 3. 3xVy 0(xy = 1) 4. VxSy((x + y = 2) A (2x - y = 1)) 5. Vx #03y(xy = 1) 6. 3x(x2 = 2) 7. Vx3y(x2 = y) 8. Vx3y (x = y) 9. 3x3y (x + y + y + x) 10. Vx3zty(z = xty) 11. 3x3y ((x + 2y = 2)^(2x + 4y = 5)) 12. Vx3y(x + y = 1)
The truth value of a statement can be determined by evaluating the statement in the context of the given universe of discourse.
3xVy(xy = 0): False. The statement is saying that for any x and y in the universe of discourse, the product of x and y must be zero. This is impossible in the set of real numbers.
3x (x2 = -1): False. The statement is saying that for any x in the universe of discourse, the square of x must be -1. This is impossible in the set of real numbers.
3xVy 0(xy = 1): False. The statement is saying that for any x and y in the universe of discourse, the product of x and y must be one. This is impossible in the set of real numbers.
VxSy((x + y = 2) A (2x - y = 1)): True. The statement is saying that for any x and y in the universe of discourse, the sum of x and y must be 2 and the difference between 2x and y must be 1. This is possible in the set of real numbers, so the statement is true.
Vx #03y(xy = 1): False. The statement is saying that for any x and y in the universe of discourse, the product of x and y must be one. This is impossible in the set of real numbers.
3x(x2 = 2): False. The statement is saying that for any x in the universe of discourse, the square of x must be 2. This is impossible in the set of real numbers.
Vx3y(x2 = y): False. The statement is saying that for any x and y in the universe of discourse, the square of x must be equal to y. This is impossible in the set of real numbers.
Vx3y (x = y): True. The statement is saying that for any x and y in the universe of discourse, x must be equal to y. This is possible in the set of real numbers, so the statement is true.
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a four-story office building has interior columns spaced 30 ft apart in two perpendicular directions. if the flat-roof live loading is estimated to be 30 lb>ft2 , determine the reduced live load supported by a typical interior column located at ground level.
a four-story office building has interior columns spaced 30 ft apart in two perpendicular directions
Determine the service live load for a first floor interior column direction
following ASCE-7 guidelines
Area = 20 * 25 = 500 ft^2 which is > 400 ft^2
Nominal live load on every floor = 80 psf
Hence the reduced service live load ( L )
L = Lo [ 0.25 + 15 / √AI ] ------ ( 1 )
Lo = unreduced load
AT = Tributary area = 500 * number of floors = 2000 ft^2
AI ( influence area ) = AT * number of floors = 2000 * 4 = 8000 ft^2
Lo = 1.6 * 80 psf * 2000 ft^2 = 256 kips
Input values into equation 1 above
L = 106 kips
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the cooling of hot coffee can be described by the following equation: where 1. is the mass of the coffee (in si units, kg) 2. is the heat capacity of the coffee (in si units, j/(kg c) 3. is the temperature of the coffee (in si units, c) 4. is the temperature of the room (in si units, c) 5. is the heat transfer coefficient (in si units, w/(m2 c) 6. is the surface area of the cup (in si units, m2) 7. is time (in si units, s) if room temperature is 25 c and the coffee is originally at 80 c, how long will it take the coffee to cool to 45 c if the ratio ? provide your answer in minutes.
We cannot determine the exact time it takes for the coffee to cool to 45°C without additional information. The value of hA/mC (heat transfer coefficient times surface area over mass times heat capacity) needs to be known to solve for Δt accurately.
The equation describing the cooling of hot coffee is given by:
dT/dt = -h * A * (T - T_room) / (mc)
where T is the temperature of the coffee, T_room is the temperature of the room, h is the heat transfer coefficient, A is the surface area of the cup, m is the mass of the coffee, and c is the heat capacity of the coffee.
We can solve for the time it takes for the coffee to cool from an initial temperature of 80°C to a final temperature of 45°C by integrating both sides of the equation over time, with the initial conditions T(0) = 80°C:
t = (mc / (h * A)) * ln((T_initial - T_room) / (T_final - T_room))
Plugging in the given values, we have:
t = (mc / (h * A)) * ln((80 - 25) / (45 - 25))
Since the units of t are in seconds, we can convert to minutes by dividing by 60:
t = (mc / (h * A)) * ln((80 - 25) / (45 - 25)) / 60
Note that the value of h * A / mc is given as ?, so we cannot determine the exact time it takes for the coffee to cool to 45°C without additional information.
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The cooling of hot coffee can be described by the following equation:
mehA(TT) where 1m is the mass of the coffee (in SI units, kg)
2. c is the heat capacity of the coffee (in SI units, J/kg C)
3. T is the temperature of the coffee (in SI units, C)
4. Tom is the temperature of the room (in SI units, °C)
5. h is the heat transfer coefficient in SI units, W/m O 6. As the surface area of the cup in SI units, m²)
7.ts time (in SI units, s)
#room temperature is 25°C and the coffee is originally at 80 C. how long will it take the coffee to cool to 45 Ct the ratio 10? Provide your answer in minutes.
How do you make two different denominators the same
Equivalent expressions to (4/5x+1)+(2/5x-1)
Answer.
Tha answer will be 6x/5 as a fraction
Step-by-step explanation:
As a decimal it is 1.2 cause
6/5=1 1/5= 1.2
Answer:
6/5x
Step-by-step explanation:
To find the equivalent expression, you need to simplify the expression (4/5x + 1) + (2/5x - 1) by combining like terms.
Starting with the first pair of terms:
(4/5x + 1) + (2/5x - 1)
= (4/5x) + (2/5x) + 1 - 1
= (6/5x) + 0
= 6/5x.
So, the equivalent expression for (4/5x + 1) + (2/5x - 1) is 6/5x.
Suppose an arrow is shot upward on the moon with a velocity of 58 m/s, then its height in meters after t seconds is given by h(t)=58t−0.83t^2 . Find the average velocity over the given time intervals.
[6, 7]: [6, 6.5]: [6, 6.1]: [6, 6.01]: [6, 6.001]:
Answer:
6,6.5
Step-by-step explanation:
hello!! I need help with this before Friday!!! Please may you give a good explanation and the answer too!!
Answer:
Method 1: Calculate 40% discount on original price, then subtract discount from original price.
Amount of discount = 40% of $30
= 0.40 × $30
= $12
New price = $30 - $12 = $18
Method 2:
New price = (100% - discount percentage) of original price
= 60% of original price
= 0.60 × $30
= $18
1. suppose two fair 6-sided dice, each numbered {1,2,3,4,5,6} are rolled. let m be the maximum of the two dice. find e(m) and v ar(m).
For two fair 6-sided diced that are rolled, the expected value of maximum (E(m)) is 3.5 and variance of maximum (Var(m)) is 2.91.
To find the expected value of the maximum of two dice rolls, we need to find the sum of the products of each maximum value and its probability of occurring.The maximum value of each combination of two dice rolls can range from 2 to 6, with the following probabilities:
Maximum of 2: 1/36
Maximum of 3: 2/36
Maximum of 4: 3/36
Maximum of 5: 4/36
Maximum of 6: 5/36
So the expected value (E(m)) can be calculated as:
E(m) = (2 × 1/36) + (3 × 2/36) + (4 × 3/36) + (5 × 4/36) + (6 × 5/36)
E(m) = 3.5
To find the variance of the maximum (Var(m)), we need to use the formula for variance of a discrete random variable:
Var(m) = E((m - E(m))²)
Var(m) = E((m - 3.5)²)
Var(m) = (2 - 3.5)² × 1/36 + (3 - 3.5)² × 2/36 + (4 - 3.5)² × 3/36 + (5 - 3.5)² × 4/36 + (6 - 3.5)² × 5/36
Var(m) = 2.91
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The students in a club are selling flowerpots to raise money. Each flowerpot sells for $15.
Part B
The goal of the students in the club was to raise $500. They sold 43 flowerpots. By what amount did the students exceed their goal of raising $500? Show or explain all your work.
Find an autonomous differential equation with all of the following properties:
equilibrium solutions at y=0 and y=3,
y' > 0 for 0
y' < 0 for -inf < y < 0 and 3 < y < inf
dy/dx = ______
dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.
The autonomous differential equation that satisfies all of the given properties is dy/dx = (y-3)(y+3). This equation has two equilibrium solutions at y = 0 and y = 3, and is positive for -inf < y < 0, and negative for 0 < y < 3, and positive for 3 < y < inf.
To demonstrate this, let's consider the equation at y=-3. Since y=-3 is less than 0, the equation can be simplified to dy/dx = 6. Since 6 is positive, y' is also positive, meaning that y is increasing. Similarly, if y=3, dy/dx = 0 which is neither positive nor negative, so y remains constant. Finally, for y>3, dy/dx = -6, which is negative, so y is decreasing.
Therefore, dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.
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CAN SOMEONE PLEASEEEE HELP I GOT TO TURN THIS IN IN LIME 5 MINUTES
Answer:
a. They are proportional
b. 11
Step-by-step explanation: They table is said to be proportional because all their ratios are the same/equal.
b. 5.5 multiplied by 2 is 11.( cross check the other values of wet dog food by multiplying the values by 2)
What is the value of y in the solution to the system of equations?
1/3 x + 1/4y =1
2x - 3y = -30
-8
-3
3
8
Answer:
y = 8
Step-by-step explanation:
2/3 x+1/2y = 2
2/3 x - y = -10
3/2y = 12
y = 8
The depth of a local river averages 20 ft, which is represented as |−20|. In January, it measured 6 ft deep, or |−6|, and in July, it was 22 ft, or |−22|. What is the difference between depths in January and July?
2 feet
28 feet
14 feet
16 feet
The difference between depths in January and July is 18 feet.
What is the difference between the depths in January and July?We know that the average depth of the river is 20 feet.
We know that the depth on January was 6ft, while the depth on July was 22ft, the difference is just the subtraction between these two values, we will get:
Difference = 22 feet - 6 feet = 16 feet.
Then the correct option is the fourth one, the difference between the depths is 16 ft.
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Gerald has just been hired for a new job and wants to work out his budget for each month. The health insurance plan he selected has an average monthly premium of $297 . The average monthly cost of his electric bill is $281 and the phone/internet/cable package he wants costs an average of $220 each month. If his monthly salary is $2800 , estimate the amount of money he will have after paying these bills each month.
The amount of money he will have after paying these bills each month is $2002.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The health insurance plan he selected has an average monthly premium of $297 .
The average monthly cost of his electric bill is $281.
The phone/internet/cable package he wants costs an average of $220 each month.
The monthly salary is $2800.
Now,
Total cost.
= 297 + 281 + 220
= 798
Now,
The amount remaining.
= 2800 - 798
= $2002
Thus,
The amount of money he will have is $2002.
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6 ^ { 4 x - 3 } = - 4
The solution to the equation [tex] {6}^{(4x - 3)} = - 4[/tex] is x = 0.3019.
To solve the equation [tex]{6}^{(4x - 3)} = - 4[/tex], we need to isolate the variable x. Here are the steps to solve this equation:
First, we need to take the logarithm base 6 of both sides of the equation. This will help us to isolate the exponent.
log6 [tex]{6}^{(4x - 3)}[/tex]= log6 -4
Use the logarithmic property that [tex] log(b) {b}^{x} = x[/tex] to simplify the left-hand side.
4x - 3 = log6 -4
Use a logarithmic table or calculator to find the value of the right-hand side.
4x - 3 = log6 -4
4x - 3 = -1.7924
Finally, we can isolate the variable x by adding 3 to both sides of the equation and then dividing both sides by 4.
4x = 3 - 1.7924
4x = 1.2076
x = 1.2076 ÷ 4
x = 0.3019
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please help me quick
All the reasoning of the statement is given below.
CA ≅ CB, by the congruent triangles.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given:
CD bisects AB at D.
CD⊥AB
To prove: CA ≅ CB:
Statement 2:
AD ≅ BD
Reason 2:
Definition of segment bisector.
Statement 3:
CD ⊥ AB
Reason 3:
Given.
Statement 6:
CD ≅ CD.
Reason 6:
Reflexive property of congruence.
Statement 7:
ΔCAB ≅ ΔCBD
Reason 7:
Congruent by the criterion SAS.
Therefore, CA ≅ CB.
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Mike and Emily are brother and sister. Mike has as many brothers as sisters, and Emily has three times as many brothers as sisters. How many boys and girls are there in this family?
The total number of brothers and sisters in the family can be represented by the equation 4x + 2.
How many boys and girls are there in this family?Number of brothers and sisters mike has = x
Number of brothers and sisters Emily has = 3x
Mike = 1 brother
Emily= 1 sister
Total boys and girls are there in this family = Number of brothers and sisters mike has + Number of brothers and sisters Emily has + Mike + Emily
= x + 3x + 1 + 1
= 4x + 2
Hence, there are 4x + 2 boys and girls in the family including mike and Emily.
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Swimming pool A is being filled at a rate of 4 inches every 12 minutes. Swimming pool B is being filled at a rate of 7 inches every 18 minutes. What is the difference of the rates at which the pools are being filled in inches per minute ?
Answer:
So, the difference of the rates at which the pools are being filled is 1/18 inch per minute.
Step-by-step explanation:
We can find the rate of filling of each pool by dividing the inches filled per hour by the number of minutes it takes to fill them.
Rate of Pool A = 4 inches / 12 minutes = 1/3 inch per minute
Rate of Pool B = 7 inches / 18 minutes = 7/18 inch per minute
The difference in the rates of filling the two pools is:
(7/18) - (1/3) = (7/18) - (6/18) = 1/18 inch per minute.
So, the difference of the rates at which the pools are being filled is 1/18 inch per minute.
A flower is 92 inches tall. In one week, it grew 4 1 inches. How tall is the flower at the end of the week? Write in simplest form.
At the end of the week, the flower is 96.5 inches tall.
graph the inequality 3x - 2y > 4
A graph of the inequality 3x - 2y > 4 is shown in the image attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).In this exercise, we would use an online graphing calculator to plot the given inequality 3x - 2y > 4 as shown on the graph attached below. Based on the graph (see attachment), we can logically deduce that the solution to the given inequality is the shaded region.
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Set Up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y tan? X, Y = 3, and X = 0 about the line Y = 3. 3 3 tan- 2x)2 ax
The volume of the solid obtained by rotating the region in the first quadrant can be found using the method of cylindrical shells.
The volume of the solid is obtained by rotating the region in the first quadrant bounded by the curves y = tan(x), y = 3, and x = 0 about the line y = 3.
The formula for the volume is:
V = 2π ∫[0,a] (3 - tan(x)) (3 - y) dxwhere a is the value of x such that y = tan(x) intersects y = 3, and y = tan(x) is the equation of the upper boundary of the region being rotated. To find a, we need to solve the equation tan(x) = 3 for x. The exact value of a can then be plugged into the integral.
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Help please which graph shows…. Look at image
Option C is the correct representation of the solution of the inequality equation.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. Any of the symbols for inequality, including greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).
Given the equation, [tex]\frac{x^{2} + 9x - 22 }{x + 4}[/tex] ≥ 0
factors of x² + 9x - 22 are,
x² + 11x - 2x - 22
x(x + 11) - 2(x + 11) = (x + 11)(x - 2)
[tex]\frac{(x + 11)(x - 2)}{x +4}[/tex] ≥ 0
x - 2 ≥ 0
x ≥ 2
so the line should be greater than and equal to 2.
so x + 11 ≥ 0
x ≥ -11
1/(x + 4) ≥ 0 or x + 4 < 0
x < -4
and line varies from,
-4 > x ≥ 11
graph of inequality is between -11 and -4 in which -4 is not included and -11 is included.
only the graph of option C satisfied the conditions.
Hence Option C is correct.
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I don’t understand the algebra. My brain has stopped working can someone explain how they got 100x + 900 = 112x + 504
Answer:
100x+900−900=112x
Step-by-step explanation:
100x+900−900=112x+504−900
an adult with twice the mass of the student is also on the ride and remains stuck to the wall while the ride is rotating just like the student. derive an algebriac expression to show that the mass of the rider does not determine if the ride will remain stationaty against the wall while the ride is rotating
The force acting on the adult and the student, both stuck to the wall, is determined by their weight and the centripetal force acting on them. This means that the net force acting on both of them must be equal to zero.
The quadratic equation in LaTeX:
$ax^2 + bx + c = 0$
The weight of an object is proportional to its mass, and the centripetal force acting on an object is proportional to its mass and the square of its velocity.
Therefore, the ratio of the force acting on the adult to the force acting on the student will be equal to the square of the ratio of their masses and the square of the ratio of their velocities.
Let the mass of the student be 'm' and the mass of the adult be '2m'. Then, the ratio of the forces acting on them will be (2m) / m * (v_adult / v_student)^2, where 'v' represents velocity.
Since the ride remains stationary against the wall for both the student and the adult, this means that the net force acting on both of them must be equal to zero, i.e. their weight must be balanced by the centripetal force acting on them.
Thus, (2m) / m * (v_adult / v_student)^2 = 1.
This equation shows that the mass of the rider does not determine if the ride will remain stationary against the wall while rotating. The ride's velocity and the distribution of mass on the ride will determine whether it remains stationary or not, not the mass of the rider.
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